To find the volume of the solid shape with the given dimensions (6 cm, 6 cm, 6 cm, 12 cm, 6 cm, 6 cm), we first need to understand the configuration of these measurements.
Given these values, it appears that they represent the lengths of the edges of a geometric solid, specifically a rectangular prism. The dimensions of the rectangular prism (or cuboid) can be understood as its length, width, and height.
Given that:
- The three equal sides are likely the dimensions of the base or height,
- While the side measured at 12 cm could be its length or depth.
Assuming the arrangement goes as follows:
- Length = 12 cm
- Width = 6 cm
- Height = 6 cm
We can use the formula for the volume of a rectangular prism: \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \] Substituting in the values: \[ \text{Volume} = 12 , \text{cm} \times 6 , \text{cm} \times 6 , \text{cm} = 432 , \text{cm}^3 \]
However, this value is not listed in the options you provided. Let’s check the calculation for other possibilities, as the values might be used in different combinations or geometric forms.
If we misunderstood the arrangement, we can consider other combinations, but every straightforward interpretation leads back to the volume being \(432 , \text{cm}^3\).
Reviewing the answer options provided (42 cm³, 360 cm³, 648 cm³, 654 cm³), none of these match the calculated volume of 432 cm³.
Under the assumption that no errors were made with interpretation, or if there’s another defined arrangement of these edges leading to a different structure (for example, if it is a specific solid shape composed of multiple prisms or any other geometric considerations), please provide clarifications.
Nonetheless, based on standard interpretation of given dimensions forming a rectangular prism, the calculated volume is \(432 , \text{cm}^3\), which does not align with the answer choices given.
If you intended to describe a different solid (such as a complex shape with these edges), additional detail is needed to provide the correct volume calculation.